On the existence of global vortex rings. (English) Zbl 0457.76020


76B47 Vortex flows for incompressible inviscid fluids
35R05 PDEs with low regular coefficients and/or low regular data
35B99 Qualitative properties of solutions to partial differential equations


Zbl 0282.76014
Full Text: DOI


[1] S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I–II, Comm. Pure Appl. Math.12 (1959), 623–727;17 (1964), 35–92. · Zbl 0093.10401
[2] A. Ambrosetti and P. Rabinowitz,Dual variational methods in critical point theory and applications, J. Functional Analysis14 (1973), 349–381. · Zbl 0273.49063
[3] M. S. Berger and L. E. Fraenkel,Global free boundary problems and the calculus of variations in the large, Lecture Notes in Mathematics503, Springer-Verlag, pp. 186–192.
[4] L. E. Fraenkel and M. S. Berger,A global theory of steady vortex rings in an ideal fluid, Acta Math.132 (1974), 13–51. · Zbl 0282.76014
[5] B. Gidas, W.-M. Ni and L. Nirenberg,Symmetry and related properties via maximum principle, Comm. Math. Phys.68 (1979), 209–243. · Zbl 0425.35020
[6] D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977. · Zbl 0361.35003
[7] W.-M. Ni,Some minimax principles with applications in nonlinear elliptic boundary value problems and global vortex flow, Ph.D. Thesis, New York University, June 1979.
[8] W.-M. Ni,Some minimax principles and their applications in nonlinear elliptic equations, J. Analyse Math.37 (1980), 248–275. · Zbl 0462.58016
[9] M. H. Protter and H. F. Weinberger,Maximum Principles in Differential Equations, Prentice-Hall, 1967. · Zbl 0153.13602
[10] P. Rabinowitz,Variational methods and nonlinear eigenvalue problems, inEigenvalues in Nonlinear Problems, C.I.M.E., 1974, pp. 141–195.
[11] M. M. Vainberg,Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, 1964
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